Bad quality mesh, Narrow tris as result of Ctrl+t (exporting stl file)
So here is what I did and it worked for me.

After I got the original mesh (left figure on top), I use Remesh modifier with mode set to Smooth. This way I got a very high quality mesh with only quads. When I triangulated the high quality quad mesh none of them became narrow.
However, the size of the .stl file becomes very large. Therefore, I use Decimate modifier to lower the number of faces and keep checking the mesh quality with 3D printing add-on.